Question

The null and alternate hypotheses are:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

A random sample of 23 items from the first population showed a mean of 107 and a standard deviation of 12. A sample of 15 items for the second population showed a mean of 102 and a standard deviation of 5. Use the 0.025 significant level.

1. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)

2. State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places.)

3. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

4. What is your decision regarding the null hypothesis? Use the 0.03 significance level.

Answer 1

(A) degree of freedom = minimum of (n1-1) or (n2-1)

we have n1 = 23 and n2 = 15

so, df = 15-1 = 14

(B) it is a right tailed hypothesis

so, t critical = T.INV(alpha,df)

setting alpha = 0.025 and df = 14, we get

t critical = 2.145

Decision rule:- we reject Ho, if t statistic is greater 2.145

(C) Using TI 84 calculator

press stat then tests then 1-sampTTest

enter the data

x1 = 107, s1 = 12, n1 = 25, x2 = 102, s2 = 5 and n2 = 15

Pooled: No

press enter, we get

t statistic = 1.835

(D) Do not reject the Ho because the test statistic is not greater than t critical value of 2.145